{"id":"https://openalex.org/W1990304174","doi":"https://doi.org/10.1137/060673400","title":"Consensus Optimization on Manifolds","display_name":"Consensus Optimization on Manifolds","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1990304174","doi":"https://doi.org/10.1137/060673400","mag":"1990304174"},"language":"en","primary_location":{"id":"doi:10.1137/060673400","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060673400","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://orbi.uliege.be/handle/2268/9491","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016288250","display_name":"Alain Sarlette","orcid":"https://orcid.org/0000-0001-5909-437X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alain Sarlette","raw_affiliation_strings":["alain.sarlette@ulg.ac.be and r.sepulchre@ulg.ac.be#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"alain.sarlette@ulg.ac.be and r.sepulchre@ulg.ac.be#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067642477","display_name":"Rodolphe Sepulchre","orcid":"https://orcid.org/0000-0002-7047-3124"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Rodolphe Sepulchre","raw_affiliation_strings":["Universit\u00e9 de Li\u00e8ge - ULi\u00e8ge > D\u00e9p. d'\u00e9lectric., \u00e9lectron. et informat. (Inst.Montefiore) > Syst\u00e8mes et mod\u00e9lisation >  >"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Li\u00e8ge - ULi\u00e8ge > D\u00e9p. d'\u00e9lectric., \u00e9lectron. et informat. (Inst.Montefiore) > Syst\u00e8mes et mod\u00e9lisation >  >","institution_ids":["https://openalex.org/I157674565"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":19.4612,"has_fulltext":false,"cited_by_count":266,"citation_normalized_percentile":{"value":0.99284069,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"48","issue":"1","first_page":"56","last_page":"76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7331103086471558},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6559173464775085},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5309395790100098},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.49859023094177246},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.48294204473495483},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46845173835754395},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4469861686229706},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3982320725917816},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.26938962936401367}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7331103086471558},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6559173464775085},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5309395790100098},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.49859023094177246},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.48294204473495483},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46845173835754395},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4469861686229706},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3982320725917816},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26938962936401367},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/060673400","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060673400","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.5042","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.5042","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.montefiore.ulg.ac.be/services/stochastic/pubs/2009/SS09a/ss_sicon2008.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.245.6764","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.6764","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0811.4275v1.pdf","raw_type":"text"},{"id":"pmh:oai:generic.eprints.org:577493","is_oa":false,"landing_page_url":"http://publications.eng.cam.ac.uk/577493/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922847","display_name":"Cambridge University Engineering Department Publications Database","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:orbi.ulg.ac.be:2268/9491","is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/9491","pdf_url":null,"source":{"id":"https://openalex.org/S4306400651","display_name":"Open Repository and Bibliography (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 48 (1), 56-76 (2009-01)","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":{"id":"pmh:oai:orbi.ulg.ac.be:2268/9491","is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/9491","pdf_url":null,"source":{"id":"https://openalex.org/S4306400651","display_name":"Open Repository and Bibliography (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 48 (1), 56-76 (2009-01)","raw_type":"http://purl.org/coar/resource_type/c_6501"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1704609","https://openalex.org/W85112348","https://openalex.org/W152416454","https://openalex.org/W1501994587","https://openalex.org/W1578099820","https://openalex.org/W1592546441","https://openalex.org/W1804110266","https://openalex.org/W1805843217","https://openalex.org/W1894990513","https://openalex.org/W1971035315","https://openalex.org/W1983718735","https://openalex.org/W1984420702","https://openalex.org/W1997648297","https://openalex.org/W2001133651","https://openalex.org/W2015410655","https://openalex.org/W2017587562","https://openalex.org/W2025800439","https://openalex.org/W2035469609","https://openalex.org/W2045512849","https://openalex.org/W2064404969","https://openalex.org/W2075385642","https://openalex.org/W2084371156","https://openalex.org/W2107396783","https://openalex.org/W2109409043","https://openalex.org/W2111749847","https://openalex.org/W2116630866","https://openalex.org/W2118420048","https://openalex.org/W2125668987","https://openalex.org/W2126323506","https://openalex.org/W2128084896","https://openalex.org/W2128924023","https://openalex.org/W2130518506","https://openalex.org/W2133776435","https://openalex.org/W2139504267","https://openalex.org/W2147631863","https://openalex.org/W2152556309","https://openalex.org/W2154834860","https://openalex.org/W2155965955","https://openalex.org/W2162876202","https://openalex.org/W2165744313","https://openalex.org/W2168132433","https://openalex.org/W2195081763","https://openalex.org/W2292988288","https://openalex.org/W2562983303","https://openalex.org/W4231784839","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2035564297","https://openalex.org/W4380087116","https://openalex.org/W2363631255","https://openalex.org/W4353055780","https://openalex.org/W2367207206","https://openalex.org/W2061430950","https://openalex.org/W2168546361","https://openalex.org/W4237344571","https://openalex.org/W2108861020","https://openalex.org/W2378960857"],"abstract_inverted_index":{"The":[0,18,34,85,122],"present":[1],"paper":[2],"considers":[3],"distributed":[4],"consensus":[5,35],"algorithms":[6,53,74],"that":[7,104],"involve":[8],"N":[9],"agents":[10,19],"evolving":[11],"on":[12,95,148],"a":[13,31,45,68,91,118],"connected":[14],"compact":[15],"homogeneous":[16],"manifold.":[17],"track":[20],"no":[21],"external":[22],"reference":[23],"and":[24,83,111,127],"communicate":[25],"their":[26],"relative":[27],"state":[28],"according":[29],"to":[30,50,54,90],"communication":[32,79],"graph.":[33],"problem":[36],"is":[37,75,81,88,105,140],"formulated":[38],"in":[39,108],"terms":[40],"of":[41,44,71,114,120],"the":[42,58,64,66,72,78,100,128,144,149],"extrema":[43],"cost":[46,86],"function.":[47],"This":[48],"leads":[49],"efficient":[51],"gradient":[52,73],"synchronize":[55],"(i.e.,":[56,62],"maximizing":[57],"consensus)":[59,65],"or":[60],"balance":[61],"minimizing":[63],"agents;":[67],"convenient":[69],"adaptation":[70],"used":[76],"when":[77],"graph":[80],"directed":[82],"time-varying.":[84],"function":[87],"linked":[89],"specific":[92],"centroid":[93],"definition":[94],"manifolds,":[96],"introduced":[97],"here":[98],"as":[99,135],"induced":[101],"arithmetic":[102],"mean,":[103],"easily":[106],"computable":[107],"closed":[109],"form":[110],"may":[112],"be":[113],"independent":[115],"interest":[116],"for":[117],"number":[119],"manifolds.":[121],"special":[123],"orthogonal":[124],"group":[125],"$SO(n)$":[126],"Grassmann":[129],"manifold":[130],"$\\text{{\\it":[131],"Grass\\/}}(p,n)$":[132],"are":[133],"treated":[134],"original":[136],"examples.":[137],"A":[138],"link":[139],"also":[141],"drawn":[142],"with":[143],"many":[145],"existing":[146],"results":[147],"circle.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":19},{"year":2012,"cited_by_count":17}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}